1Why Ultrasound Physics Matters

Every sonographer needs physics knowledge for four core reasons:

1. Creating diagnostic images — understanding physics helps you produce clear, accurate pictures
2. Identifying artifacts — things that appear on screen that aren’t real structures; physics tells you why they happen
3. Equipment maintenance — you can recognize when something is wrong with the machine
4. Registry exams — the SPI tests this directly

2Key Historical Figures

3The Pulse-Echo Technique

This is the foundation of all ultrasound imaging.

Step-by-step process

1. The transducer sends a short sound pulse into the body
2. Sound travels through tissue at 1,540 m/s
3. It hits a boundary (like your carotid artery wall) and some bounces back
4. The echo returns to the transducer
5. The machine times how long the return took → calculates depth
6. That depth gets plotted as a bright dot on screen
7. Repeat thousands of times per second → real-time image

4Speed of Sound & the 13 µs Rule

The machine assumes ALL soft tissue conducts sound at this speed. It uses this to calculate depth. If the actual speed is very different (bone, air), the image distorts.

The 13-Microsecond Rule

• 1 microsecond = 0.000001 seconds
• Sound travels ~1 cm deep (round trip) in 13 µs
• 26 µs return = 2 cm deep
• 39 µs = 3 cm deep
• Pattern: depth in cm = return time ÷ 13

5Real-Time B-Mode Imaging

B-Mode = Brightness Mode. The standard 2D gray-scale image you see on every scan.

• Each returning echo = a bright dot on screen
• Stronger echo = brighter dot
• The transducer sweeps many narrow lines called scan lines across the tissue
• All those lines together = one complete frame
• ~30 frames per second = smooth, real-time video motion

6Scan Formats

7Doppler Ultrasound

Doppler detects and displays blood flow. It works on the Doppler Effect — the same reason an ambulance siren sounds higher-pitched as it approaches and lower as it leaves.

• Red blood cells moving toward the transducer → higher frequency echo
• Moving away → lower frequency echo
• Machine detects this frequency shift → displays as flow information

8Direct vs. Indirect Proportionality

• Direct proportion: When A goes up, B goes up. (More depth → more time for echo to return)
• Indirect / inverse proportion: When A goes up, B goes down. (Higher frequency → less penetration depth)

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Forgetting 13 µs is round-trip — sound goes TO the structure AND comes back
2. Mixing up Curie and Doppler — Curie = crystals = transducer. Doppler = flow detection
3. Thinking B-Mode and Doppler are the same — B-mode shows anatomy; Doppler shows movement
4. Assuming all tissue is the same — the 1,540 m/s rule is an assumption; bone and air break it, causing artifacts

1What IS Sound?

Sound is a mechanical wave. It needs a physical medium (tissue, water, gel) to travel through. Unlike light, sound CANNOT travel through a vacuum (empty space).

Two rules to always remember

• Sound is a mechanical, longitudinal wave
• Sound requires a medium to travel — no medium, no sound

2Longitudinal vs. Transverse Waves

Sound waves are longitudinal — molecules move back and forth in the same direction the wave travels.

• Compression = areas where molecules are pushed together
• Rarefaction = areas where molecules are spread apart

3The 7 Characteristics of Sound

1. Frequency 🔵 SPI

What it is: The number of complete wave cycles that occur in one second.

Unit: Hertz (Hz), kilohertz (kHz), or megahertz (MHz)

• Human hearing: 20 Hz – 20,000 Hz (20 kHz)
• Diagnostic ultrasound: 2 MHz – 15 MHz (above human hearing = “ultra” sound)
• Carotid transducer is typically 5–10 MHz

Clinical impact:

• Higher frequency = better image detail (resolution) BUT less depth penetration
• Lower frequency = worse detail BUT deeper penetration
• Carotid is superficial → use high frequency → sharp, detailed image

2. Period 🔵 SPI

What it is: The time it takes to complete ONE full wave cycle. The exact opposite of frequency.

Unit: Seconds (usually microseconds, µs)

The relationship: Period and frequency are INVERSELY proportional.

• Higher frequency → shorter period
• Lower frequency → longer period
• Formula: Period = 1 ÷ Frequency

3. Wavelength 🔵 SPI

What it is: The physical length of one complete wave cycle — measured from one compression to the next.

Unit: Millimeters (mm) in tissue

• Higher frequency → shorter wavelength → better resolution
• Lower frequency → longer wavelength → worse resolution but deeper penetration

4. Propagation Speed 🔵 SPI

What it is: How fast sound travels through a medium.

Unit: Meters per second (m/s)

Key numbers to memorize:

5. Amplitude 🟣 BOTH

What it is: The maximum variation (peak height) of a wave — how “tall” the wave is. Represents the strength or loudness of the sound.

Unit: Decibels (dB)

Why it matters: Amplitude relates directly to how bright echoes appear on your screen. Stronger echoes (higher amplitude returning) = brighter dots on the image.

Set by: The sound source (transducer output). You can adjust this with the gain and output power controls on the machine.

6. Power 🔵 SPI

What it is: The total amount of energy produced by the transducer per unit of time.

Unit: Watts (W) or milliwatts (mW)

Key relationship: Power is proportional to amplitude squared.

• Double the amplitude → 4× the power
• Power relates to bioeffects and patient safety

7. Intensity 🟣 BOTH

What it is: Power concentrated into a specific area. How much energy hits a given spot.

Unit: Watts per centimeter squared (W/cm²)

Formula: Intensity = Power ÷ Area

Why it matters: Intensity is the most important measure for patient safety. High intensity focused on a small area can cause bioeffects (heat, cavitation). This is why ALARA is your guiding principle.

4Key Relationships to Know

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Thinking frequency changes propagation speed — it doesn't. Speed = tissue property only
2. Forgetting the trade-off — higher frequency ALWAYS means less penetration. Always.
3. Mixing up power and intensity — power is total energy output; intensity is energy per area
4. Forgetting ALARA — it's not just a rule, it's a testable clinical concept
5. Confusing amplitude and frequency — amplitude = wave height (strength); frequency = wave speed (cycles per second)

1Pulse Wave (PW) vs Continuous Wave (CW) Transducers

Ultrasound transducers come in two fundamental types based on whether they pulse the sound on/off or transmit continuously.

2Pulse Wave vs Continuous Wave Doppler

Doppler ultrasound measures blood flow velocity. There are two modes, each with strengths and trade-offs.

The trade-off in plain English

• PW Doppler: “I can tell you exactly WHERE the flow is, but only if it’s slow enough.”
• CW Doppler: “I can measure ANY flow velocity, but I can’t tell you where along the beam it’s coming from.”

3The SS Rule (Stiffness & Speed)

A useful memory aid for how propagation speed depends on tissue properties:

The SS rule is just a mnemonic for the relationships from Lecture 1 and Lecture 2 — stiffness has the dominant effect on propagation speed. Bone is fast (very stiff). Air is slow (no stiffness). Soft tissue lands at the standard 1,540 m/s.

4Speed vs Velocity

Physics formality that comes up on the SPI exam.

5Wave Properties (Brief Refresh)

A quick reminder of relationships from earlier lessons. Full coverage in Lecture 2 and the Exam 1 Review.

• Frequency & period: inversely related (period = 1 / frequency)
• Frequency & wavelength: inversely related (λ = c ÷ f)
• Higher frequency: shorter wavelength, better resolution, but MORE attenuation → less penetration
• Lower frequency: longer wavelength, less resolution, but LESS attenuation → deeper penetration

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Thinking CW transducers can make images — they can’t. They’re always transmitting, with no listening time for echoes
2. Confusing PW Doppler with CW Doppler trade-offs — PW has spatial info but aliases. CW has no spatial info but no aliasing
3. Using “speed” and “velocity” interchangeably on exams — velocity requires direction, speed doesn’t. SPI holds the line on this
4. Forgetting the SS rule emphasizes STIFFNESS over density — both affect speed, but stiffness dominates
5. Thinking high frequency is always better — it gives better resolution but attenuates faster, so it can’t reach deep structures

1The Pulse-Echo Principle

Pulsed ultrasound creates diagnostic images using pulse-echo technique: the transducer sends out a sound pulse, then waits to receive echoes that bounce back from tissue boundaries.

The cycle for every pulse

1. Transducer emits a brief pulse of sound
2. Sound travels through tissue at ~1,540 m/s
3. At tissue boundaries, some sound reflects back as echoes
4. Transducer receives the echoes and converts them to electrical signals
5. Machine processes the signals to build the image

2How the Machine Calculates Depth

The ultrasound machine knows the speed of sound in soft tissue (1,540 m/s). It can measure the time between sending a pulse and receiving the echo. From those two facts, it calculates how deep the reflector was.

Why divide by 2?

The sound travels to the reflector AND back. The total round-trip time covers twice the actual depth. To get the actual depth, divide the time (or the calculated distance) by 2.

Worked concept (no math required for exams)

• Speed in soft tissue: 1,540 m/s (a constant the machine assumes)
• Time measured: round-trip time of the echo
• Divide by 2: because the sound traveled there AND back

3Pulse Parameters (Brief Refresh)

The pulse parameters covered in this session are detailed elsewhere. Here's a quick reference table:

4Amplitude, Power & Intensity

Three closely-related variables that describe the "strength" of a sound wave:

How they relate

• Power ∝ Amplitude² — power is proportional to amplitude squared. Double the amplitude = 4× the power.
• Intensity = Power ÷ Area — power and intensity are directly related. Area and intensity are indirectly related (smaller area = higher intensity).

5Power Adjustment & Patient Safety

The ultrasound machine automatically sets appropriate power levels based on the body part being scanned. Operators should generally NOT modify the power settings upward — doing so could potentially harm patients through tissue heating or mechanical effects.

When to REDUCE power

• Fetal exams — developing tissue is more sensitive
• Brain vessel exams (TCD) — sensitive structures, prolonged exposure risk
• Any exam where you can get adequate imaging with less power

6Spatial & Temporal Peak Intensities

Intensity is measured in different ways depending on where in the beam and when in the pulse cycle you measure it.

Spatial dimension (across the beam)

• Spatial Peak (SP) — highest intensity at any single point in the beam
• Spatial Average (SA) — intensity averaged across the entire beam cross-section

Temporal dimension (across time)

• Temporal Peak (TP) — highest intensity during the pulse
• Pulse Average (PA) — intensity averaged across just the pulse duration
• Temporal Average (TA) — intensity averaged across the whole listen-and-transmit cycle (much lower)

Combined notations (these get tested)

• SPTA — Spatial Peak / Temporal Average. The most clinically relevant for safety / heating effects.
• SPPA — Spatial Peak / Pulse Average
• SATA — Spatial Average / Temporal Average

7Attenuation (Brief Refresh)

Attenuation is the weakening of the sound beam as it travels through tissue. Three components: reflection, absorption, and scattering. Absorption is the largest contributor.

8Half-Value Layer Thickness

Half-value layer thickness (HVL) is the depth at which the sound wave's intensity is reduced to HALF of its original value. It's a specific way of quantifying how attenuating a tissue is at a given frequency.

Why HVL matters

• Different frequencies attenuate at different rates → different HVLs
• Higher frequency → SHORTER HVL (intensity drops to half quickly)
• Lower frequency → LONGER HVL (intensity drops to half more slowly)
• HVL is shorter in highly-attenuating tissues, longer in low-attenuation media

Quick example concept (no math required)

If a 5 MHz beam has an HVL of about 1.5 cm in soft tissue:

• At 1.5 cm depth: intensity is 50% of original
• At 3.0 cm depth: intensity is 25% (half of half)
• At 4.5 cm depth: intensity is 12.5%

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Forgetting the "÷2" in the distance formula — sound travels there AND back. The round-trip time is double the one-way time.
2. Thinking power and intensity are the same thing — power is total energy/time. Intensity is power per unit area. Same power, smaller area = higher intensity.
3. Adjusting power upward to "see better" — the machine sets safe defaults. Don't increase. Adjust gain, depth, or frequency instead.
4. Confusing SPTA with TI — SPTA is an intensity measurement. Thermal Index (TI) is a different (related) safety output — don't mix them up.
5. Thinking HVL is a fixed number — HVL changes with frequency AND with the tissue. There's no single HVL.
6. Forgetting the frequency-penetration trade-off — higher frequency = better resolution AND less penetration. You can't maximize both.

1What Happens at a Tissue Boundary

When a sound wave reaches a boundary between two tissues, ONE of three things happens to its energy. Sound cannot be created or destroyed — it has to go somewhere.

2Three Sound Components

At every boundary, three terms describe the parts of the sound wave:

3Perpendicular vs. Oblique Incidence

The angle at which sound hits a boundary determines how reliably it reflects back to the transducer.

Perpendicular (90°) incidence

• Sound hits the boundary head-on (perpendicular to the surface)
• Guarantees reflection back to the transducer
• Required condition for reliable imaging

Oblique (angled) incidence

• Sound hits the boundary at any non-perpendicular angle
• Reflection bounces away at the matching angle (law of reflection) — may not return to the transducer at all
• Results in less reliable imaging

4Acoustic Impedance & Reflection

Two conditions must BOTH be met for reflection to occur:

1. The sound must hit the boundary at 90° (perpendicular)
2. The two tissues must have different acoustic impedances

Quick refresher: acoustic impedance (Z)

Acoustic impedance describes a tissue’s resistance to sound transmission. Formula: Z = density × propagation speed. Unit: rayls.

• Bigger impedance mismatch → more reflection → brighter echo
• Smaller impedance mismatch → less reflection → weaker echo
• Identical impedances → no reflection at all

5Intensity Reflection & Transmission Coefficients

IRC (Intensity Reflection Coefficient)

IRC is the percentage of the incident intensity that reflects at a boundary.

ITC (Intensity Transmission Coefficient)

ITC is the percentage of the incident intensity that transmits forward into the next tissue.

Calculating IRC

The IRC formula uses the acoustic impedances of the two tissues at the boundary:

Three patterns to remember

• Equal impedances (Z₁ = Z₂): IRC = 0% → ITC = 100% (all sound transmits)
• Slightly different: small IRC → most sound transmits, weak echo
• Very different (tissue/air, tissue/bone): large IRC → most sound reflects, strong echo, nothing left to image deeper

6Three Components of Attenuation

As sound travels through tissue, it gets weaker over distance. This weakening is called attenuation, and it has three causes:

• Reflection — sound bouncing back at boundaries
• Absorption — sound energy converted to heat (the largest contributor)
• Scattering — sound dispersed in many directions

7Scattering

Scattering happens when sound waves encounter non-smooth or heterogeneous boundaries. Instead of reflecting in one direction (like a mirror), the sound disperses in many directions.

Why scattering is GOOD for imaging

• Lets you visualize tissue texture — the inside of organs, not just their surfaces
• Allows assessment of organ integrity — homogeneous vs. heterogeneous patterns
• Without scattering, organs would look like empty outlines

Types of scattering

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Forgetting reflection needs BOTH conditions — 90° incidence AND impedance mismatch. Either alone won’t produce reliable reflection
2. Thinking most sound reflects — only ~1% does. The other 99% transmits and creates more reflections at deeper boundaries
3. Confusing backscatter and Rayleigh scattering — backscatter is a direction (sound returning toward the transducer); Rayleigh is a TYPE (scatterer much smaller than the wavelength, like RBCs)
4. Forgetting IRC + ITC = 100% — they must always add up. If you know one, you can find the other
5. Treating scattering as bad — it’s actually GOOD. Without scattering, organs would have no internal texture
6. Thinking absorption is just a small piece of attenuation — it’s the LARGEST cause in soft tissue

1The Law of Reflection

When sound waves hit a tissue boundary, they reflect — and the way they reflect follows a predictable rule:

Why 90° incidence is ideal for imaging

When sound hits a boundary at 90° (perpendicular), the reflection bounces straight back to the transducer. That’s what produces the strongest, clearest echoes.

• 90° incidence → echo returns directly to transducer → strong, bright signal
• Oblique (angled) incidence → echo bounces away at an angle → weaker or missing signal

2Specular Reflection

A specular reflector is a smooth, large boundary that reflects sound like a mirror — in one predictable direction.

• Examples: the diaphragm, vessel walls, organ surfaces (capsule of the liver, kidney capsule), bladder wall
• Behavior: reflects sound at one specific angle (determined by the law of reflection)
• Imaging implication: very angle-dependent — if you’re not perpendicular, the echo doesn’t reach the transducer

3Refraction

Refraction is the bending of a sound wave as it crosses a boundary between two tissues. Unlike reflection (where sound bounces back), refraction means the sound continues forward — but in a new direction.

Both conditions must be met

When refraction does NOT occur

• At 90° (normal) incidence — even if speeds differ, sound continues straight through without bending
• When propagation speeds are equal — even at oblique angles, no bending happens

4Snell’s Law

Snell’s Law of Refraction is the mathematical formula that describes how much sound bends when crossing a boundary.

What the law tells us conceptually

• The amount of bending depends on the ratio of propagation speeds in the two media
• The bigger the speed difference, the more the wave bends
• If sound enters a slower medium → wave bends toward the normal (perpendicular)
• If sound enters a faster medium → wave bends away from the normal

5Refraction Artifacts

Refraction can produce artifacts — features in your image that don’t correspond to real anatomy. The machine assumes sound traveled in a straight line, so when refraction bends the beam, structures appear in the wrong location.

Common refraction artifacts

• Edge shadow / refraction shadow: a dark line at the edge of a curved structure (like the edge of a cyst or fluid-filled vessel) where the beam refracts away
• Displacement of structures: the imaged location of a deep structure shifts because the beam bent on the way there
• Duplicated images: sometimes a structure appears twice on the screen (less common but possible)

6Contrast Media in Ultrasound

Ultrasound contrast agents are microbubbles (typically gas-filled, encased in a thin shell) injected intravenously to enhance image quality in specific situations.

Purpose

• Enhance tissue perfusion visualization (how well blood is flowing into a tissue)
• Improve image clarity for masses that look very similar to surrounding tissue
• Help characterize lesions in liver, kidney, heart

Why it works

The microbubbles have a hugely different acoustic impedance from blood and tissue. They reflect sound very strongly, making blood-filled structures “light up” on the image.

7Harmonics

Harmonic imaging is a technique that improves image quality by using multiples of the transmitted frequency rather than just the original frequency.

How it works

• The transducer transmits at a fundamental frequency (e.g., 3 MHz)
• Tissue distorts the wave nonlinearly as it travels, generating harmonic frequencies (multiples like 6 MHz, 9 MHz)
• The transducer receives ONLY the harmonic frequencies (typically the second harmonic)
• The image is built from these harmonic echoes

Why it improves image quality

• Reduces artifacts — many noise sources don’t generate harmonics, so they get filtered out
• Better lateral resolution — the harmonic beam is narrower than the fundamental beam
• Clearer images in difficult patients (obese, gas-bowel patterns, etc.)

8Wave Interference (Wave Addition)

When two sound waves meet, they combine — their amplitudes add together at every point. The result depends on whether they’re “in step” or “out of step.”

Constructive interference

• Two waves are in phase (peaks aligned with peaks, troughs with troughs)
• Amplitudes ADD together
• Result: a bigger, stronger wave

Destructive interference

• Two waves are out of phase (peaks aligned with troughs)
• Amplitudes CANCEL out
• Result: a smaller wave, or complete cancellation

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Forgetting refraction needs BOTH conditions — different speeds AND oblique incidence. Either alone won’t cause it
2. Mixing up specular and non-specular reflectors — specular = smooth, mirror-like, angle-dependent. Non-specular = rough/small, scatters in many directions, less angle-dependent
3. Trying to memorize Snell’s Law equation — focus on the conditions for refraction and how to avoid it, not the math
4. Treating contrast media as a major exam topic — it’s covered for awareness; not heavily tested. Don’t over-invest study time here
5. Thinking constructive interference makes waves “louder” — it makes them HIGHER amplitude. Loudness is more about perception; amplitude is the physics
6. Forgetting that 90° incidence prevents refraction — even when speeds differ, sound goes straight through at perpendicular incidence

1Acoustic Variables

An acoustic variable is any property of the medium that changes as sound passes through it. There are three:

• Pressure — local force per area; rises in compression, falls in rarefaction
• Density — how tightly packed molecules are; higher in compression, lower in rarefaction
• Particle motion (distance) — how far molecules move from their resting position as the wave passes

2Sound Frequency Ranges

Sound is divided into three frequency ranges based on whether humans can hear it:

3Propagation Speed (Review)

Propagation speed is constant within a single medium and depends on two physical properties:

• Stiffness — directly related to speed (stiffer = faster). Has the GREATEST influence.
• Density — inversely related to speed (denser = slower)

4Wavelength & Frequency Relationships

Wavelength (λ), frequency (f), and propagation speed (c) are connected by one essential formula:

Key relationships

• Frequency & period: inversely related (period = 1 / frequency)
• Frequency & wavelength: inversely related (higher f → shorter λ)
• Speed & wavelength: directly related (faster medium → longer λ)

5Pulse Repetition Period & Frequency

PRP (Pulse Repetition Period)

Pulse repetition period is the time from the start of one pulse to the start of the next — including the “listening time” for echoes to return.

• Unit: microseconds (µs) or milliseconds (ms)
• Set by: the imaging depth — deeper imaging requires longer PRP (more time to wait for echoes)

PRF (Pulse Repetition Frequency)

Pulse repetition frequency is the number of pulses fired per second.

• Unit: Hertz (Hz) or kilohertz (kHz)
• Typical range: 1,000 – 10,000 Hz (1–10 kHz)

How depth affects PRP and PRF

• Deeper imaging → longer PRP needed → lower PRF
• Shallower imaging → shorter PRP works → higher PRF

6Spatial Pulse Length (SPL)

Spatial pulse length is the physical length of one pulse from start to finish — how much “space” the pulse occupies as it travels through tissue.

Why SPL matters

SPL directly determines axial resolution:

• Shorter SPL → better axial resolution
• Longer SPL → worse axial resolution

To shorten SPL: use higher frequency (shorter wavelength) and/or fewer cycles per pulse (achieved through damping).

7Duty Factor

Duty factor is the percentage of time the transducer is actually transmitting (firing pulses) vs. listening for echoes.

Typical values

• Pulsed-wave imaging: very low — typically < 1% (transducer is mostly listening)
• Continuous-wave Doppler: 100% (always transmitting)

How depth affects duty factor

Increasing depth increases PRP (longer wait for echoes) → duty factor decreases.

8Acoustic Impedance

Acoustic impedance (Z) is a material’s resistance to sound transmission. It’s what determines how much sound reflects at a tissue boundary.

When sound encounters two materials with different impedances, some sound reflects (echoes) and some transmits forward. The bigger the impedance mismatch, the more reflection.

9Reflection vs. Refraction

Both happen at tissue boundaries, but they require different conditions and produce different effects.

Types of reflectors

• Specular reflector: a smooth, large boundary that reflects sound in one direction (like a mirror). Examples: organ surfaces, vessel walls, diaphragm.
• Non-specular (diffuse) reflector: a rough or small boundary that scatters sound in many directions. Examples: organ parenchyma (liver, kidney tissue).
• Rayleigh scatterers: a special case — structures much smaller than the wavelength (like red blood cells) that scatter sound in all directions equally. The basis of Doppler signal from blood.

10Attenuation

Attenuation is the progressive weakening of the sound beam as it travels through tissue. It happens due to three causes:

• Absorption — sound energy converted to heat (the largest contributor)
• Reflection — sound bouncing back at boundaries
• Scattering — sound dispersed in many directions

Attenuation coefficient

The attenuation coefficient describes how fast attenuation happens per unit depth, in dB/cm.

Decibel sign convention

• Negative dB: sound weakening (attenuation — the normal case)
• Positive dB: sound strengthening (amplification — when the machine boosts the signal)

11Intensity Reflection Coefficient (IRC)

Intensity reflection coefficient is the fraction of intensity that reflects at a boundary. It depends entirely on the impedance mismatch between the two tissues.

• Equal impedances → IRC = 0 (no reflection, all sound transmits)
• Slightly different impedances → small IRC (most sound transmits, weak echo)
• Very different impedances (tissue/air, tissue/bone) → large IRC (most sound reflects, strong echo)

12Power, Amplitude & Intensity (Review)

Quick refresher on the relationships between these (Lecture 2 covered these in detail):

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Mixing up reflection and refraction conditions — reflection needs impedance mismatch; refraction needs speed mismatch AND non-perpendicular angle
2. Confusing PRF with frequency — frequency is set by the transducer (MHz); PRF is set by depth (kHz). Different things.
3. Forgetting that depth changes both PRP and PRF — they move together because they’re inversely related
4. Thinking density has the biggest effect on propagation speed — it doesn’t. Stiffness is the dominant factor.
5. Treating SPL and PRP as the same thing — SPL is the physical length of one pulse; PRP is the time between pulses
6. Forgetting the attenuation rule of thumb — dB/cm ≈ MHz ÷ 2. A 10 MHz beam attenuates ~5 dB/cm in soft tissue.

1The Piezoelectric Effect

The piezoelectric effect is what makes ultrasound possible. It is a two-way conversion between electrical and mechanical (sound) energy in certain crystals.

• Apply voltage to a crystal → it vibrates and produces sound waves (transmit mode)
• Sound waves return and hit the crystal → it generates voltage (receive mode)

2Piezoelectric Materials

Several materials exhibit the piezoelectric effect. The most important one in modern ultrasound:

• PZT (lead zirconate titanate): the standard synthetic ceramic used in modern transducers. Strong piezoelectric effect, durable, easily manufactured to specific thickness
• Quartz: natural crystal, used in older transducers. Largely replaced by PZT
• Other natural materials: tourmaline, Rochelle salt — of historical interest only

3Components of a Transducer

A modern transducer is more than just a crystal. It has multiple layers, each with a specific job:

1. Piezoelectric element (PZT crystal)

The active element — the part that actually vibrates and produces / receives sound. Usually PZT, ground to a precise thickness.

2. Matching layer

A layer placed in front of the PZT crystal (on the patient side). Its job: reduce impedance mismatch between the crystal and the patient’s skin/tissue.

3. Backing (damping) material

A layer placed behind the PZT crystal (away from the patient). Its job: absorb sound waves traveling backward so they don’t bounce around inside the transducer.

4Acoustic Impedance & the Matching Layer

Acoustic impedance is a material’s resistance to sound transmission. It depends on the material’s density and the speed of sound in it.

When sound encounters a boundary between two materials with different impedances, some of it reflects. The bigger the impedance mismatch, the more reflection — and the less sound makes it across.

The matching layer’s rule

The matching layer’s impedance must fall between the PZT’s impedance and the skin’s impedance. This step-down design lets sound transition gradually instead of slamming into a hard impedance wall.

5Bandwidth & Quality Factor

Bandwidth

Bandwidth is the range of frequencies present in a single ultrasound pulse. Transducers don’t produce one pure frequency — they produce a band of frequencies centered on the operating frequency.

• Broad bandwidth: contains many different frequencies; produces a short pulse
• Narrow bandwidth: contains few frequencies; produces a longer pulse

Quality Factor (Q)

Quality factor (Q) describes how “pure” the transducer’s frequency output is. It’s the inverse of bandwidth.

• High Q: narrow bandwidth, more sensitive, longer pulse — good for Doppler / continuous wave
• Low Q: broad bandwidth, less sensitive, shorter pulse — good for B-mode imaging (better axial resolution)

6Operating Frequency

The transducer’s operating frequency is the dominant frequency it produces. Two physical properties of the PZT crystal determine it:

• Propagation speed of sound through the PZT material
• Thickness of the PZT crystal

PZT crystal thickness

• Typical thickness: 0.2 to 1 mm
• Thickness is generally half the wavelength of sound in the material
• Thinner crystal → higher operating frequency
• Thicker crystal → lower operating frequency

7Decibels & Sound Attenuation

Decibels (dB) describe the relative strength of a sound wave. Sonographers see them in attenuation discussions:

• Negative dB: sound beam is weakening (attenuation — the normal case in tissue)
• Positive dB: sound beam is strengthening (amplification — e.g., when the machine boosts the signal)

8Transducer Safety

Transducers are clinical electronics in direct contact with patients. Damaged equipment is a real safety hazard.

Before EVERY use

• Inspect the transducer face for cracks in the housing
• Inspect cables for frays, exposed wires, or damage
• Make sure the cable is not tangled, twisted, or dragging on the floor

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Thinking the matching layer’s impedance equals the body’s — it’s BETWEEN the PZT and the body, not equal to either
2. Forgetting the piezoelectric effect goes both ways — the same crystal both transmits AND receives
3. Confusing bandwidth and Q factor — they’re inversely related: broad bandwidth = low Q, narrow bandwidth = high Q
4. Not realizing damping has a trade-off — it improves axial resolution but reduces sensitivity
5. Skipping the safety check — cracked transducers and frayed cables can shock patients. Inspect every time

1Anatomy of a Sound Beam

A sound beam from a transducer doesn’t travel as a perfect cylinder. It forms an hourglass shape — narrowing toward a focal point, then diverging into the far field.

Three regions of the beam

• Near field (Fresnel zone): the converging region from the transducer face down to the focus. Beam narrows here.
• Focus (focal zone): the narrowest point of the beam — where image quality is best.
• Far field (Fraunhofer zone): the diverging region beyond the focus. Beam widens with depth.

Huygens’ principle & diffraction

Sound waves don’t travel in perfectly straight lines. As they leave the transducer they spread out — this is diffraction. Huygens’ principle explains it: every point along a wavefront acts as a source of new wavelets, and those wavelets combine to produce the next wavefront. This is why the beam has the shape it does.

2Near Zone Length

Near zone length (NZL) is the distance from the transducer face to the focal point — i.e., how deep into the body the focus naturally falls.

Two factors determine NZL

• Transducer diameter: larger diameter → longer near zone
• Operating frequency: higher frequency → longer near zone

Far zone divergence

How much the beam spreads out in the far field also depends on diameter and frequency:

• Higher frequency → narrower beam, less divergence in the far field
• Larger diameter → less divergence (beam stays more parallel)

3Axial Resolution

Axial resolution is the ability to distinguish two structures that lie along the beam’s path — one in front of the other.

What controls axial resolution

Axial resolution is determined by spatial pulse length (SPL) — shorter pulse = better axial resolution. SPL depends on:

• Frequency (higher → shorter wavelength → shorter SPL)
• Number of cycles per pulse (fewer cycles → shorter SPL)
• Wavelength in tissue

4Lateral Resolution

Lateral resolution is the ability to distinguish two structures lying side-by-side — perpendicular to the beam’s direction of travel.

What controls lateral resolution

Lateral resolution depends on beam width. The narrower the beam, the better the lateral resolution.

Three ways to improve lateral resolution

1. Focus the beam at the depth of interest — puts the narrowest part of the beam where you’re imaging
2. Use a higher frequency transducer — produces a narrower beam in the far field
3. Use a smaller diameter transducer — narrower starting beam

5Slice Thickness (Elevational) Resolution

Slice thickness resolution — also called elevational resolution — is the ability to distinguish structures that lie perpendicular to the imaging plane. It accounts for the fact that the beam itself has thickness — the “slice” isn’t infinitely thin.

Slice thickness is the least important of the three spatial resolutions because it’s the hardest to control — but it can cause artifacts (especially partial volume effect, where structures inside the slice blur together).

6Beam Focusing

Since lateral resolution is best at the focal point, controlling WHERE the focal point falls is critical. There are two eras of focusing:

Conventional focusing (older)

Used in older single-element mechanical transducers. Focal depth was fixed — chosen by the probe’s physical construction.

• Acoustic lens: a curved plastic lens in front of the crystal that focuses the beam
• Curved piezoelectric element: a crystal ground into a concave shape that focuses the beam by geometry
• Acoustic mirror: a reflector inside the transducer housing that focuses the beam

Electronic focusing (modern)

Used in modern array transducers. The focal depth is adjustable — the operator can place the focus wherever they need it.

Achieved by firing the array’s individual crystal elements at slightly different times. The timing pattern (called a delay sequence) creates a wavefront that converges at the chosen depth.

7Types of Transducers

Mechanical transducers (obsolete)

Older transducers used a single piezoelectric element that was physically moved (oscillated or rotated) to sweep the beam. They are no longer used in modern ultrasound because they had no electronic focusing, no beam steering, and mechanical wear over time.

Array transducers (modern)

Modern transducers use an array — many small piezoelectric elements arranged together. The machine fires them in coordinated patterns to electronically focus and steer the beam.

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Mixing up axial and lateral resolution — axial is along the beam (front-to-back), lateral is across the beam (side-by-side)
2. Forgetting where lateral resolution is best — it’s at the FOCAL POINT, not at the surface or in the far field
3. Thinking larger diameter = better lateral resolution — it’s the opposite. Smaller diameter narrows the beam
4. Forgetting that mechanical transducers are obsolete — exam questions still ask about them, but you won’t see them in clinic
5. Confusing the near zone with the focal zone — the near zone is the WHOLE region from the probe to the focus; the focal zone is just the narrowest point

1Linear Sequential (Switched) Array

The simplest array transducer. A row of crystal elements arranged in a straight line; the machine activates small groups of adjacent elements one group at a time.

How it works

• Crystal elements arranged in a straight row
• The machine fires a small group of adjacent elements (the active aperture), then shifts the group by one element and fires again
• Each firing produces one scan line; many scan lines combined form the image

Image format

• Rectangular image — wide near-field, equally wide far-field
• Field of view matches the physical footprint of the transducer

2Curved / Curvilinear (Convex) Array

Same firing principle as a linear array, but the elements are arranged along a curved surface instead of a straight line.

Image format

• Trapezoidal (fan-shaped) image — narrow near-field, wider far-field
• Wider field of view at depth than a linear array

3Phased Array

A small, compact array where ALL elements fire on every scan line, but with carefully controlled timing differences to STEER the beam electronically.

How it works — electronic beam steering

• All elements fire on every line — but with slight time delays between them
• Firing one edge slightly before the other tilts the wavefront’s direction (constructive interference at an angle)
• By varying the timing pattern, the beam “sweeps” across a sector from a single physical position

Image format

• Sector image (pie-shape) — narrow point at the transducer, fanning out with depth
• Small footprint — fits between ribs and other small acoustic windows

4Annular Phased & Vector Arrays

Annular phased array

• Elements arranged in concentric rings (like a bullseye) instead of a row
• Time delays between rings create radially symmetric focusing — the focus narrows in all directions equally
• Excellent lateral resolution, but typically MECHANICALLY steered (not electronically) because rings can’t steer the beam sideways

Vector array

• Hybrid of phased + linear — elements in a row, but with electronic steering capability
• Image format: trapezoid with sector-like steering — looks like a flat-top sector
• Wider far-field than linear, smaller footprint than curved

5Electronic Focusing & Dynamic Focusing

Electronic focusing (transmit focus)

By firing the OUTER elements of the array slightly before the INNER elements, all the wavefronts converge at a chosen depth. That depth becomes the focal point.

Dynamic focusing (receive focus)

• Adjusts the focus continuously and automatically as the echo returns from increasing depths
• Each receive-focus depth gets its own timing pattern
• Improves resolution at every depth without operator input

Aperture

• Aperture = the size of the active group of elements firing at one time
• Larger aperture → better lateral resolution at depth, but worse near-field resolution
• Modern machines dynamically adjust aperture (“dynamic aperture”) for optimal resolution at each depth

6Apodization & Sub-Dicing

Apodization

• Firing the outer elements with lower amplitude than the inner elements
• Reduces side lobes — stray sound energy leaking off the main beam
• Trade-off: slightly wider main beam (small loss of lateral resolution) in exchange for fewer side-lobe artifacts

Sub-dicing

• Physically splitting each element into smaller sub-elements (typically 2-4 sub-elements per element)
• Reduces grating lobes — a specific kind of side artifact caused by element spacing
• Sub-elements fire together as a unit; the splitting just changes the sound-field geometry

7Multiple Transmit Focus

Most transducers transmit at ONE focal depth per scan line. Multiple transmit focus fires the SAME scan line several times, each at a different focal depth, then combines the results into one composite line.

Benefit

• Excellent lateral resolution at multiple depths simultaneously
• Image is sharp throughout, not just at one focal zone

The cost — frame rate

8Broken Elements & Image Quality

When one or more elements in an array fail, image quality degrades in predictable ways depending on the array type.

✨Cheat Sheet

⚠Common Beginner Mistakes

1. Confusing how linear vs phased arrays fire — linear: small group fires per line, group shifts. Phased: ALL elements fire per line with timing differences
2. Mixing up apodization and sub-dicing — apodization (amplitude) reduces side lobes. Sub-dicing (physical splitting) reduces grating lobes. Different problems, different solutions
3. Thinking electronic focusing means inner elements fire first — it’s the opposite. Outer first, inner last. The outer waves have a longer path to the focal point and need a head start
4. Forgetting multiple transmit focus costs frame rate — you can’t get sharp resolution at multiple depths AND high frame rate. Pick the right tool for the right anatomy
5. Confusing broken element behavior by array type — linear/curved: visible stripe. Phased: whole image degrades. Different failure signatures
6. Overstudying transducers — 7% of the exam. Know the basics and move on